Let x and y be independent, non-negative, continuous random variables with respective hazard rate functions λx(t) and λy (t) and set w = min(x, y ). (a) determine the distribution function of w in terms of those of x and y . (b) show that λw (t), the hazard rate function of w, is given by λw (t) = λx(t) + λy (t).

In a probability experiment, karen flipped a coin 76 times. the coin landed on heads 32 times. what percentage of the coin flips resulted in tails? round to the nearest percent. a. 58% b. 65% c. 42% d. 60%

The perimeter of a rectangle is greater than or equal to 74 meters. if the length is 25 meters, the minimum width of the rectangle is meters.

Astudent draws two parabolas on graph paper. both parabolas cross the x-axis at (-4, 0) and (6,0). the y-intercept of thefirst parabola is (0, –12). the y-intercept of the second parabola is (0-24). what is the positive difference between the avalues for the two functions that describe the parabolas? write your answer as a decimal rounded to the nearest tenth.